Probability Rules Study Guide

Introduction to Probability

Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Basic Probability Rules

1. Addition Rule: The probability of the union of two events, denoted as P(A or B), is given by:

   P(A or B) = P(A) + P(B) - P(A and B)

2. Multiplication Rule: The probability of the intersection of two independent events, denoted as P(A and B), is given by:

   P(A and B) = P(A) * P(B)

3. Complement Rule: The probability of the complement of an event A, denoted as P(A'), is given by:

   P(A') = 1 - P(A)

4. Conditional Probability: The probability of event A given that event B has occurred, denoted as P(A|B), is given by:

   P(A|B) = P(A and B) / P(B)

Additional Probability Rules

1. Independent Events: Two events A and B are independent if the occurrence of one event does not affect the occurrence of the other. In this case, P(A and B) = P(A) * P(B).
2. Mutually Exclusive Events: Two events A and B are mutually exclusive if they cannot occur at the same time. In this case, P(A or B) = P(A) + P(B).
3. Law of Total Probability: If B1, B2, ..., Bn form a partition of the sample space S, then for any event A:

   P(A) = P(A|B1) * P(B1) + P(A|B2) * P(B2) + ... + P(A|Bn) * P(Bn)

Example Problems

1. A fair six-sided die is rolled. What is the probability of rolling an even number or a number less than 3?

2. A jar contains 5 red, 3 blue, and 2 green marbles. If a marble is selected at random, what is the probability of selecting a red or a green marble?